Estimates of Carrying Capacity with Quantile Random Forest Models

¹ Biomark, Inc.

1 Introduction

1.1 QRF Model

We developed a quantile random forest (QRF) model with paired fish and habitat data from a number of sites around the Columbia River Basin (Table 1.1). We developed separate QRF models for each species, using the haitat covariates shown in Table 1.2. Please note that the total volume of large wood has been scaled by the site length, so it is in units of m\(^3\) / 100 m.

Table 1.1: Number of sites with fish/habtiat data that went into QRF model.

Watershed	Chinook	Steelhead
Asotin	0	12
Entiat	54	71
John Day	36	106
Lemhi	17	48
Minam	15	15
Upper Grande Ronde	88	120
Total	210	372

Table 1.2: Selected habitat covariates for QRF model.

Metric	Name	MetricCategory	DescriptiveText
CU_Freq	Channel Unit Frequency	ChannelUnit	Number of channel units per 100 meters.
SlowWater_Pct	Slow Water Percent	ChannelUnit	Percent of wetted area identified asSlow Water/Pool channel units.
Sin_CL	Sinuosity Via Centerline	Complexity	Ratio of the wetted centerline length (Site Length Wetted) and the straight line distance between the start and end points of the wetted centerline. Generated by the River Bathymetry Toolkit (RBT)
WetBraid	Wetted Channel Braidedness	Complexity	Ratio of the total length of the wetted mainstem channel plus side channels and the length of the mainstem channel.
WetSC_Pct	Wetted Side Channel Percent By Area	Complexity	Ratio of the total area of side channel unit areas (both small and large) divided by the total area of channel unit polygons.
FishCovSome	Fish Cover: Some Cover	Cover	Percent of wetted area with some form of fish cover
FishCovSome	Fish Cover: Some Cover	Cover	Percent of wetted area with some form of fish cover
UcutLgth_Pct	Percent Undercut by Length	Cover	The percent of the wetted streambank length that is undercut.
Q	Discharge	Size	The sum of station discharge across all stations. Station discharge is calculated as depth x velocity x station increment for all stations except first and last. Station discharge for first and last station is 0.5 x station width x depth x velocity.
WetWdth_Int	Wetted Width Integrated	Size	Average width of the wetted polygon for a site.
SubEstGrvl	Substrate Est: Coarse and Fine Gravel	Substrate	Percent of coarse and fine gravel (2-64 mm) within the wetted site area.
SubEstGrvl	Substrate Est: Coarse and Fine Gravel	Substrate	Percent of coarse and fine gravel (2-64 mm) within the wetted site area.
avg_aug_temp	Avg. August Temperature	Temperature	Average predicted daily August temperature from NorWest, averaged across the years 2002-2011.
LWVol_Wet	Large Wood Volume: Wetted	Wood	Total volume of large wood pieces within the wetted channel, scaled by site length.

The relative importance of the habitat covariates are shown in Figure 1.1.

Figure 1.1: Relative importance of each habitat covariate, colored by species.

Figure 1.2: Relative importance of each habitat covariate, by species.

Partial dependence plots show the marginal effect of each covariate by displaying the predicted capacity as that covariate changes, assuming all the other covariates remain fixed at their average values. The partial dependence plots are shown for Chinook (Figure 1.3) and steelhead (Figure 1.4).

Figure 1.3: Partial dependence plots for Chinook QRF model.

Figure 1.4: Partial dependence plots for steelhead QRF model.

From this QRF model, we made capacity predictions at every CHaMP site, after averaging the habitat metrics across years for sites visited more than once. We extrapolated those predictions of capacity at CHaMP sites to every master sample points using various globally available attributes assigned to every master sample point (including each CHaMP sites).

2 Methods

2.1 Watershed Maps

We created maps depicting the entire watershed (Lemhi, Pahsimeroi and Upper Salmon) showing QRF predicted summer juvenile capacity in units of fish / m\(^2\).

2.2 Geomorphic Reaches

We took our QRF extrapolation estimates at each master sample point, and determined which points fell into each geomorphic reach within each watershed. Then we examined the distribution of capacity estimates within each reach, and the average capacity for each reach.

2.3 Capacity at MRA sites

We used the QRF model to predict capacity at MRA sites that were sampled with DASH in 2018. We used the predicted 90th quantile as a proxy for carrying capacity.

3 Results

3.1 Watershed Maps

## [1] "unzipping..."
## [1] "unzipping..."
## [1] "unzipping..."

## [1] "unzipping..."
## [1] "unzipping..."
## [1] "unzipping..."

3.2 Geomorphic Reaches

The distribution of capacity predictions within each geomorphic reach is shown in Figures 3.1 and 3.2. Figures 3.3, 3.4 and 3.5 are maps depicting the average capacity within each geomorphic reach.

Figure 3.1: Violin plots showing the distribution of Chinook capacity estimates for master sample points within each geomorphic reach in each watershed.

Figure 3.2: Violin plots showing the distribution of steelhead capacity estimates for master sample points within each geomorphic reach in each watershed.

Figure 3.3: Geomorphic reaches in the Lemhi colored by average capacity (fish per m). Note different scales for each species.

Figure 3.4: Geomorphic reaches in the Pahsimeroi colored by average capacity (fish per m). Note different scales for each species.

Figure 3.5: Geomorphic reaches in the upper Salmon colored by average capacity (fish per m). Note different scales for each species.

3.3 Capacity at MRA sites

Here are some options to help understand what factors are driving high or low capacity within each MRA reach.

Figure 3.6: Scatterplot of covariates and Chinook parr capacity, colored by MRA site. The facet order of covariates corresponds to their relative importance.

Figure 3.7: Boxplots showing distribution of covariates in each MRA site, colored by their average Chinook parr capacity. The facet order of covariates corresponds to their relative importance.

The following are bar plots, split by MRA site. Within each MRA site, the habitat reaches are ordered lowest capacity to highest, and the bars are also colored that way. The height of each bar shows the value of that habitat covariate.

Figure 3.8: Partial dependence plots of the Chinook parr QRF model, showing the measured values of the covariates for each habitat reach within a particular MRA site. Note that the y-axis shows predictions of capacity on a linear density scale (fish / m).

Figure 3.9: Partial dependence plots of the Chinook parr QRF model, showing the measured values of the covariates for each habitat reach within a particular MRA site. Note that the y-axis shows predictions of capacity on a linear density scale (fish / m).

Figure 3.10: Partial dependence plots of the Chinook parr QRF model, showing the measured values of the covariates for each habitat reach within a particular MRA site. Note that the y-axis shows predictions of capacity on a linear density scale (fish / m).

Figure 3.11: Partial dependence plots of the Chinook parr QRF model, showing the measured values of the covariates for each habitat reach within a particular MRA site. Note that the y-axis shows predictions of capacity on a linear density scale (fish / m).